Step 1 :
Divide $ 16790 $ by $ 11790 $ and get the remainder

$$ 16790 : 11790 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

The remainder is positive ($ 5000 > 0 $), so we will continue with division.

Step 2 :
Divide $ 11790 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11790 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1790 } \text{ ) } $$

The remainder is still positive ($ 1790 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1790 } $ and get the remainder

$$ 5000 : 1790 = 2 \text{ ( remainder is } \color{blue}{ 1420 } \text{ ) } $$

The remainder is still positive ($ 1420 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1790 $ by $ \color{blue}{ 1420 } $ and get the remainder

$$ 1790 : 1420 = 1 \text{ ( remainder is } \color{blue}{ 370 } \text{ ) } $$

The remainder is still positive ($ 370 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1420 $ by $ \color{blue}{ 370 } $ and get the remainder

$$ 1420 : 370 = 3 \text{ ( remainder is } \color{blue}{ 310 } \text{ ) } $$

The remainder is still positive ($ 310 > 0 $), so we will continue with division.

Step 6 :
Divide $ 370 $ by $ \color{blue}{ 310 } $ and get the remainder

$$ 370 : 310 = 1 \text{ ( remainder is } \color{blue}{ 60 } \text{ ) } $$

The remainder is still positive ($ 60 > 0 $), so we will continue with division.

Step 7 :
Divide $ 310 $ by $ \color{blue}{ 60 } $ and get the remainder

$$ 310 : 60 = 5 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 8 :
Divide $ 60 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 60 : \color{blue}{ \boxed { 10 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

GCD Calculator